Jean-Claude Trichet, president of the European Central Bank, has called it 'brutal'; Airbus boss Tom Enders says it is 'life-threatening'; and French President Nicolas Sarkozy has even warned that it could provoke 'economic war'. The relentless decline in the dollar may appear to be a loss of prestige for a White House pledged to uphold a 'strong dollar policy'; but the real pain is being felt thousands of miles away, in Europe.

From rapper Jay-Z flourishing €500 notes in his latest video, to Opec mutterings about pricing oil in euros instead of depreciating dollars, there are a growing number of anecdotal signs that the greenback is going out of fashion.

For a country long unchallenged as the world's sole economic superpower, this might appear to be an alarming vote of no confidence. Treasury secretary Hank Paulson was provoked into stressing last month that 'the dollar has been the world's reserve currency since World War II and it's been that for a reason. We are the biggest economy in the world, we are as open as any economy to investment, to trade, and we've had stable economic policies.'

As long as it doesn't get out of hand, and become what central bankers call 'disorderly', the decline in the greenback is in fact one of the few bright spots in the economic landscape for the White House. The sell-off is not new - the dollar has been steadily losing value since 2002, and has shed about 20 per cent of its value against the currencies of the US's major trading partners. That has made exports more competitive, boosting the fortunes of the struggling rust-belt industries that have long whinged about the dominance of China.

'The devaluation's working. The contribution of net exports to GDP is at a 30-year high - it's having the desired effect,' says Russell Jones, economist at RBC Capital Markets. And Britain's post-war economic experience suggests clinging to an overvalued currency for the sake of saving face is rarely a sound economic strategy. For America's trading partners in Europe, the fact that the euro is suddenly the preferred currency in the world of hip-hop is hardly a comfort. Coming against the background of a deteriorating economic outlook, it will exacerbate the impact of the looming US downturn. And since Beijing allows the yuan scant leeway to appreciate against the dollar, much of the pain is being felt in the eurozone, with its traditionally strong export sectors.

If Airbus is struggling, an army of much smaller manufacturers will also be feeling the pinch - at the same time as banks are making it tougher to borrow. For the UK, with its disproportionately large financial sector and overvalued housing market, the main channel by which America's woes are transmitted across the Atlantic is likely to be the turmoil in money markets, and the resulting tightening of credit. But for continental Europe, the rise in the value of the euro, which has already smashed through its previous record against the dollar, is potentially devastating.

'In the eurozone, the pips are going to squeak, and the squeaking's going to be very loud,' says David Brown, chief European economist at Bear Stearns. Already, Sarkozy has demanded action from Washington, warning the US Congress that the sliding dollar 'should not remain simply a problem for others'.

European Commission officials flew to Beijing last week to deliver the message that it is time for China to bear its share of the burden by allowing the yuan to rise. But Prime Minister Wen Jiabao pointedly refused to take the blame, saying Europe should look at the 'excessive devaluation' of the dollar to explain its woes. Within Europe, too, there is already rising political tension about the fate of the single currency, with governments demanding that the ECB take action, to keep a lid on the euro's rise. If a downturn takes hold, there is potential for a serious geopolitical clash - or even the 'economic war' envisaged by Sarkozy. 'Whenever you get a downswing, people look for scapegoats,' says Jones.

As the slowdown unfolds, much will depend on the response of Europe's consumers. The export-led recovery that has finally dragged the eurozone out of its post-dotcom slump in the past couple of years had begun to feed through into stronger household spending. But if nervous consumers pull in their horns, the upturn may come to a sudden halt. Goldman Sachs warned last week that the single currency's strength would shave 0.4 percentage points off eurozone GDP growth this year, and revised down its forecasts of growth for 2008, from 2 per cent to 1.7 per cent; though its analysts believe the euro may begin to slide in the new year.

Not everyone is pessimistic. 'Clearly, for the eurozone, export growth is going to suffer; but our view is still that domestic demand in these economies will be robust enough so that the eurozone continues to grow,' says Paul Ashworth, US economist at Capital Economics. 'Europe has also got the benefit that growth in Asia will remain strong.'

The dollar's continued weakness is only the most visible sign of a long-predicted 'rebalancing' of the global economy, from an overheating US too dependent on its spendthrift consumers, toward emerging economies that have for some years been channelling their vast export earnings abroad instead of investing them at home. 'The scale of the deficit means that it has to be offset by a dollar decline, this was always going to happen,' says Ashworth.

With the Federal Reserve poised to cut its rates again this month, Brown says the sell-off is far from over. 'It's a matter of looking at the basics - and the basics don't look good.'